Interpolation Conditions for Linear Operators and Applications to Performance Estimation Problems

The Performance Estimation Problem methodology makes it possible to determine the exact worst-case performance of an optimization method. In this work, we generalize this framework to first-order methods involving linear operators. This extension requires an explicit formulation of interpolation conditions for those linear operators. We consider the class of linear operators $x \mapsto Mx$ where matrix $M$ has bounded singular values, and the class of linear operators where $M$ is symmetric and has bounded eigenvalues. We describe interpolation conditions for these classes, i.e. necessary and sufficient conditions that, given a list of pairs $\{(x_i,y_i)\}$, characterize the existence of a linear operator mapping $x_i$ to $y_i$ for all $i$. We apply our generalized approach to the gradient method for the composed objective $h(Mx)$, where $h$ is smooth and convex, and to the Chambolle-Pock method applied to $f(x)+g(Mx)$, where $f$ and $g$ are Lipschitz and convex. We obtain new exact worst-case convergence rates for several performance criteria, including average and last iterate accuracy.Comment: 26 pages, 2 figure

Erratum to: 36th International Symposium on Intensive Care and Emergency Medicine

[This corrects the article DOI: 10.1186/s13054-016-1208-6.]

Nurses' perceptions of aids and obstacles to the provision of optimal end of life care in ICU

Contains fulltext : 172380.pdf (publisher's version ) (Open Access

TANIT 83 : a general equilibrium model for analyzing the customs duties, quotas, and price controls of the Tunisian economy

La elección de la presente problemática, aborda la población de mujeres docentes a un paso de transitar de la vida laboral a la jubilación en Ciudad Juárez, Chihuahua, mismas que después de haber entregado por lo menos 28 años de su vida productiva al cuidado de sus estudiantes, en su vida de jubilada pareciera que su destino es el cuidado de la familia a tiempo completo, la atención de sus nietos o simplemente al transcurrir de la vida como una simple contemplación de un suceso que debe ocurrir; provocando como consecuencia el abandono, la dependencia, la enfermedad, el hastío y la depresión. Abordar esta realidad social bajo el cobijo de la metodología de la animación sociocultural, permitirá empoderar a estas mujeres para ocuparse de su cuidado a través del diseño de proyectos de vida, a fin de enfrentar con éxito y dignidad su jubilación. La finalidad de la atención de esta problemática es la construcción de proyectos de vida de las docentes que van a cruzar por la etapa de la jubilación

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One of the most promising ideas to enhance the photocatalytic efficiency of the TiO2 is to couple this photocatalyst with other semiconductors. In this work, we report on the development of photo-catalytic properties of two types of composites based on TiO2 – ITO (Indium Tin Oxide) and TiO2 – ZnO deposited on conventional ceramic substrates. The samples were characterized by X-ray diffraction (XRD) and transmission Electron Microscopy (TEM). The photo-catalytic test was carried out under UV light in order to reduce/oxidize a typical textile dye (Cibacron Yellow). The experiment was carried out in a bench scale reactor using a solution having a known initial dye concentration. After optimization, we found that both nanocomposites exhibit better photocatalytic activity compared to the standard photocatalyst P25 TiO2

Corrosion behaviour of carbon steel coated with magnesium electrodeposited from methyl magnesium chloride solution

International audienc

Growth and characterization of Cu2ZnxFe1-xSnS4 thin films deposited on n-type silicon substrates

International audienceCu2FeSnS4 and Cu2ZnSnS4 ingots were successfully grown by direct melting of their high-purity constituent elements from stoichiometric compositions (copper, iron, zinc, tin and sulfide). Subsequently, thin films of CFTS and CZTS were deposited on unheated n-type silicon substrates through the vacuum evaporation method. These deposited films were sulfided for 30 min at a sulfidation treatment temperature Ts = 400 °C. The structural properties of the C (Z, F)TS thin films were studied by X-ray diffraction (XRD), Raman spectroscopy and electron backscatter diffraction (EBSD). The resulting studies suggest the existence of polycrystalline phases where CZTS has a kesterite structure and CFTS a stannite structure. Composition analysis also indicates that the synthesized C (Z,F)TS powders are close to the expected stoichiometry. A good crystallinity of CZTS followed by an increase in the average roughness value of this film is highlighted in the thin film micrographs of C (Z,F)TS. Furthermore, the Hall effect indicates that the prepared C (Z,F)TS films exhibit a manifest p-type semiconductor, and the conductivity, mobility and carrier charge concentration are higher for the CZTS thin film. The electrical conductivity of the CFTS and CZTS thin films were investigated using the impedance spectroscopy technique in the frequency range 5 Hz–13 MH. Values of activation energy are indicative of thermal activation of the conduction mechanism by jumping between localized states. Further, the analysis of the frequency and temperature dependence of the AC conductivity supports the correlated barrier hopping (CBH) model

Comparison of Proximal First-Order Primal and Primal-Dual algorithms via Performance Estimation

Selecting the fastest algorithm for a specific signal/image processing task is a challenging question. We propose an approach based on the Performance Estimation Problem framework that numerically and automatically computes the worst-case performance of a given optimization method on a class of functions. We first propose a computer-assisted analysis and comparison of several first-order primal optimization methods, namely, the gradient method, the forward-backward, Peaceman-Rachford, and Douglas-Rachford splittings. We tighten the existing convergence results of these algorithms and extend them to new classes of functions. Our analysis is then extended and evaluated in the context of the primal-dual Chambolle-Pock and Condat-V\~u methods.Comment: 5 pages, 7 figure